It is shown that in a frequency interval 95-760 kHz the effect of possible infringement of the standard hydrodynamics of smectics liquid crystals, as a rule, isn't observable. Deviations from square-law frequency dependence of factor of absorption in ultrasonic experiments are defined by processes of an acoustic relaxation. This dependence isn't neither universal, nor characteristic only for smectic A phases. Besides, her character changes at change of orientation of a wave vector concerning a magnetic field induction.

Existence of the short-range orientation order in aqueous solution of benzene is shown. The contribution of the orientations correlation into thermodynamic characteristics of dissolution is calculated. The nature of hydrophobic interactions is explained from the viewpoint of the short-range orientation order concept.

The mechanism of formation of phases in the ytterbium oxide - aluminum oxide during the hybrid sol-gel process. Revealed that the phase formation takes place according to a diffusion mechanism similar to solid-phase synthesis, but at the molecular level. (The conditions for synthesis of crystalline phase of YAG obtained by heat treatment in a hybrid sol-gel synthesis of precipitation at a temperature of ≤ 900 °.)

For the first time the electrical conduction of a thin cylindrical wire of metal was reckoning by the instantaneous method. The condition of the specular diffuse reflection of electrons off an internal surface of wire was taken as a boundary condition of the problem. The discussion of the results derived was made.

Soft cover engineering constructions represent actively developing type of technical products which find new wide application in engineering practice. Such constructions are made from fabrics, laminates, tapes and cords which on durability have come nearer to metals, but essentially it is easier than traditional constructional materials. Creation of adequate methods of calculation of such designs, advancing mathematical modeling of their functioning in actual practice is necessary. Considerable experience of engineering calculation and mathematical modeling Soft cover engineering constructions is saved up in Parachute design Industry where such workings out are spent since 50th years of the last century. In article the modeling current state in Parachute design Industry is analyzed and the problem of creation of new generation settlement methods on the basis of the equations of Lagrange of the second sort is put.

Carbon nanotube of the «armchair» type is simulated by the ideal polyhedron surface. The technique of atoms coordinates calculation is proposed permitting to vary the tube diameter. For the diphenyl molecule incapsulated into the carbon nanotube the energetic advantage of the tight contact with tube wall is shown.

The paper aims to model the behavior of a quantum mechanical system consisting of a planar wave guide made of bismuth and bismuth - antimony alloys and located in a magnetic field up to 25 T. The electronic energy spectrum in crystals is quantized, and the ultra quantum limit is reached for magnetic field of about 2 T. The passage through the planar waveguide of a monochromatic infrared radiation with quantum energy of 119 meV results in electrons jumping to Landau levels located in the conduction band. The numerical results showed a good coincidence between modeling and experimental results.

The author continues his investigation of generalized analytical properties of generalization of the Cauchy’s integral type associated with bicircle. Keywords : Cauchy’s integral, bicircle.

In this paper, the problem of constructing an analog of Δ-sets in A ∞-case. Presented to design the higher faces, we prove their existence on the homology, but also addresses the effect of the differential on this site. In proving the theorems we use the technique of SDR-situations themselves prove constructive.

Three dimension equation of liquid in ocean flows is described. Approximation on three dimension numerical grid with “frozen” turbulent exchange coefficients gets to Dirichlet’s problem for Laplace’s differential equation in a cube, and this problem is investigated. A method of solving it with prescribed uniform accuracy on a set off grid nodes in plane section of the cube is proposed. Asymptotically fast approximate methods for solving Dirichlet’s problem in the entire grid cube which use one or two additions per node are described, and explicit error estimate are given.

This article discusses options for approximation of functions of rational fractions. Here are shown the advantages and restrictions of approximation of Pade for approximation of analytically set differentiated functions. Transformation of universal topological model based on experimental data on the characteristics of a n -dimensional object received good approximation of rational fraction. The order of polynoms of numerator and denominator of rational fraction is defined. Structure of rational fraction object allows you to analyze sustainability, defining a zero denominator polynomial.

Affinely connected manifolds and there generalizations are compared with the wild classes of systems of ordinary differential equations and their properties obtain the precise differential geometry and algebraic description. Local symmetric and flat (abelian) classes of systems of ordinary differential equations are discussed. The results are used for investigation of Lagranian mechanical systems.

Proved differentiability of weak solution of inverse problem for Maxwell-Boltzmann equation which describes the distribution of electronic component discharged plasma in bounded domain of three-dimensional space. This inverse problem is investigated in terms of abstract differential equations in a Banach spaces from the viewpoint of semigroup theory. The task of determining the source function reduces to an integral equation of Voltera of the second kind. This equation is extended to a system of equations with an equation with the derivative. The study of this system allows us to obtain the condition of differentiability of the inverse problem for the original MaxwellBoltzmann’s equation.

We study the problem of expanding the reciprocal of an entire function of exponential type with simple zeros located at a half-plane in a series of partial fractions. Our main result is the development of a theorem of M. G. Krein on the properties of an entire function with simple real zeros, the inverse of which can be decomposed into simple fractions. These results demonstrate the possibility of using specific examples. The first of these is the Laplace transform, taken in a finite interval with decreasing it original. Second - regularly encountered in the analysis and probability errors integral.

We prove the formula for the roots, which give estimates of the relative growth of convex functions in Tauberian theorems.

We study the behavior of the zeros (numbered in order of nondecreasing moduli of the zeros) analytic in the disk class of functions . Obtained result: zero sets of classes where - Riesz means. Case - a class of Bergman . For works provided , where - a specified function, as , find a subsequence of indices , in which 61 and with are different.

The Cauchy problem for quasilinear differential equations system of neutral type was considered. Without assumption of uniquely solvability of corresponding linear boundary value problem the sufficient conditions of existence of solution was derived. A nonlinear part of the equation system was imposed a condition of «under linear» growth. To prove the main statement an auxiliary solution existing theorem for an operator equation with surjective but non invertible linear operator was applied.

Stages of the project development realizing the complete approach to programming training and patriotic education are considered. At all stages programming training interactive schedules in language Action Script A. Flash was carried out. However the final tasks carrying historical and cultural character, were various. The interrelation between character of final tasks and a programming learning efficiency is shown.

One of the problem’s solving mathematics sums instruction practice and theory is considered in this article (the final stage - studying, development, transformation). It drawns attention to need to proceed from the mathematics sum to the teaching and studying sum as the mean of this proceed.

The advantages and lacks of the modular approach of training, place and role in the educational standards of new generation are analyzed.

On the basis of the theory of plausibility of the Dempster-Shafer theory the algorithm of classification in a task of processing of the imperfect data with poorly divided classes is offered, the task of the coordination of opinions in various situations is decided

The basis of development of modern information society is information processes, which are widely used information and communication technologies. The introduction and use of information and communication technologies in almost all spheres of human activity has led to the emergence and development of the global information process, which in turn led to the development of informatization of education. Informatization of education is the most important condition for the reform and modernization of the education system. Secondary and higher schools teach and bring up full-fledged members of the society, which not only shape the information environment, but they themselves will live and work in this new environment. Therefore, as never before, is especially acute problem of the formation of information culture among the younger generation.